Solve y=(x-1)(n+1)

$$y = ( x - 1 ) ( n + 1 )$$

Solve for n (complex solution)

$$\left\{\begin{matrix}n=-\frac{1+y-x}{1-x}\text{, }&x\neq 1\\n\in \mathrm{C}\text{, }&y=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by n+1.

$$y=xn+x-n-1$$

Swap sides so that all variable terms are on the left hand side.

$$xn+x-n-1=y$$

Subtract x from both sides.

$$xn-n-1=y-x$$

Add 1 to both sides.

$$xn-n=y-x+1$$

Combine all terms containing n.

$$\left(x-1\right)n=y-x+1$$

The equation is in standard form.

$$\left(x-1\right)n=1+y-x$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)n}{x-1}=\frac{1+y-x}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$n=\frac{1+y-x}{x-1}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{y+n+1}{n+1}\text{, }&n\neq -1\\x\in \mathrm{C}\text{, }&y=0\text{ and }n=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by n+1.

$$y=xn+x-n-1$$

Swap sides so that all variable terms are on the left hand side.

$$xn+x-n-1=y$$

Add n to both sides.

$$xn+x-1=y+n$$

Add 1 to both sides.

$$xn+x=y+n+1$$

Combine all terms containing x.

$$\left(n+1\right)x=y+n+1$$

Divide both sides by n+1.

$$\frac{\left(n+1\right)x}{n+1}=\frac{y+n+1}{n+1}$$

Dividing by n+1 undoes the multiplication by n+1.

$$x=\frac{y+n+1}{n+1}$$

Solve for n

$$\left\{\begin{matrix}n=-\frac{1+y-x}{1-x}\text{, }&x\neq 1\\n\in \mathrm{R}\text{, }&y=0\text{ and }x=1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by n+1.

$$y=xn+x-n-1$$

Swap sides so that all variable terms are on the left hand side.

$$xn+x-n-1=y$$

Subtract x from both sides.

$$xn-n-1=y-x$$

Add 1 to both sides.

$$xn-n=y-x+1$$

Combine all terms containing n.

$$\left(x-1\right)n=y-x+1$$

The equation is in standard form.

$$\left(x-1\right)n=1+y-x$$

Divide both sides by x-1.

$$\frac{\left(x-1\right)n}{x-1}=\frac{1+y-x}{x-1}$$

Dividing by x-1 undoes the multiplication by x-1.

$$n=\frac{1+y-x}{x-1}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{y+n+1}{n+1}\text{, }&n\neq -1\\x\in \mathrm{R}\text{, }&y=0\text{ and }n=-1\end{matrix}\right.$$

Steps for Solving Linear Equation

Use the distributive property to multiply x-1 by n+1.

$$y=xn+x-n-1$$

Swap sides so that all variable terms are on the left hand side.

$$xn+x-n-1=y$$

Add n to both sides.

$$xn+x-1=y+n$$

Add 1 to both sides.

$$xn+x=y+n+1$$

Combine all terms containing x.

$$\left(n+1\right)x=y+n+1$$

Divide both sides by n+1.

$$\frac{\left(n+1\right)x}{n+1}=\frac{y+n+1}{n+1}$$

Dividing by n+1 undoes the multiplication by n+1.

$$x=\frac{y+n+1}{n+1}$$